Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x-9y &= 5 \\ -2x-5y &= 5\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-5y = 2x+5$ Divide both sides by $-5$ to isolate $y$ $y = {-\dfrac{2}{5}x - 1}$ Substitute this expression for $y$ in the first equation. $2x-9({-\dfrac{2}{5}x - 1}) = 5$ $2x + \dfrac{18}{5}x + 9 = 5$ Simplify by combining terms, then solve for $x$ $\dfrac{28}{5}x + 9 = 5$ $\dfrac{28}{5}x = -4$ $x = -\dfrac{5}{7}$ Substitute $-\dfrac{5}{7}$ for $x$ back into the top equation. $2( -\dfrac{5}{7})-9y = 5$ $-\dfrac{10}{7}-9y = 5$ $-9y = \dfrac{45}{7}$ $y = -\dfrac{5}{7}$ The solution is $\enspace x = -\dfrac{5}{7}, \enspace y = -\dfrac{5}{7}$.